Rewrite as a simplified fraction. ${0.9\overline{45} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 945.4545...\\ 10x &= 9.4545...\end{align*}}$ Subtracting the two equations, we have: ${990x = 936}$ ${x = \dfrac{936}{990}} $ ${x = \dfrac{52}{55}} $